Low Complexity Regularization of Linear Inverse Problems

Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for recovering the unknown signal is to solve a convex optimization problem that enforces some prior knowledge about its structure. This has proved efficient in many problems routinely encountered in imaging sciences, statistics and machine learning. This chapter delivers a review of recent advances in the field where the regularization prior promotes solutions conforming to some notion of simplicity/low-complexity. These priors encompass as popular examples sparsity and group sparsity (to capture the compressibility of natural signals and images), total variation and analysis sparsity (to promote piecewise regularity), and low-rank (as natural extension of sparsity to matrix-valued data). Our aim is to provide a unified treatment of all these regularizations under a single umbrella, namely the theory of partial smoothness. This framework is very general and accommodates all low-complexity regularizers just mentioned, as well as many others. Partial smoothness turns out to be the canonical way to encode low-dimensional models that can be linear spaces or more general smooth manifolds. This review is intended to serve as a one stop shop toward the understanding of the theoretical properties of the so-regularized solutions. It covers a large spectrum including: (i) recovery guarantees and stability to noise, both in terms of $\ell^2$-stability and model (manifold) identification; (ii) sensitivity analysis to perturbations of the parameters involved (in particular the observations), with applications to unbiased risk estimation ; (iii) convergence properties of the forward-backward proximal splitting scheme, that is particularly well suited to solve the corresponding large-scale regularized optimization problem

Cross-education does not accelerate the rehabilitation of neuromuscular functions after ACL reconstruction: a randomized controlled clinical trial

Purpose: Cross-education reduces quadriceps weakness 8 weeks after anterior cruciate ligament (ACL) surgery, but the long-term effects are unknown. We investigated whether cross-education, as an adjuvant to the standard rehabilitation, would accelerate recovery of quadriceps strength and neuromuscular function up to 26 weeks post-surgery. Methods: Group allocation was randomized. The experimental (n = 22) and control (n = 21) group received standard rehabilitation. In addition, the experimental group strength trained the quadriceps of the non-injured leg in weeks 1–12 post-surgery (i.e., cross-education). Primary and secondary outcomes were measured in both legs 29 ± 23 days prior to surgery and at 5, 12, and 26 weeks post-surgery. Results: The primary outcome showed time and cross-education effects. Maximal quadriceps strength in the reconstructed leg decreased 35% and 12% at, respectively, 5 and 12 weeks post-surgery and improved 11% at 26 weeks post-surgery, where strength of the non-injured leg showed a gradual increase post-surgery up to 14% (all p ≤ 0.015). Limb symmetry deteriorated 9–10% more for the experimental than control group at 5 and 12 weeks post-surgery (both p ≤ 0.030). One of 34 secondary outcomes revealed a cross-education effect: Voluntary quadriceps activation of the reconstructed leg was 6% reduced for the experimental vs. control group at 12 weeks post-surgery (p = 0.023). Both legs improved force control (22–34%) and dynamic balance (6–7%) at 26 weeks post-surgery (all p ≤ 0.043). Knee joint proprioception and static balance remained unchanged. Conclusion: Standard rehabilitation improved maximal quadriceps strength, force control, and dynamic balance in both legs relative to pre-surgery but adding cross-education did not accelerate recovery following ACL reconstruction

Manufacturing and Supply Chain Flexibility: Building an Integrative Conceptual Model Through Systematic Literature Review and Bibliometric Analysis

The purpose of this study is twofold: first, to establish the current themes on the topic of manufacturing and supply chain flexibility (MSCF), assess their level of maturity in relation to each other, identify the emerging ones and reflect on how they can inform each other, and second, to develop a conceptual model of MSCF that links different themes connect and highlight future research opportunities. The study builds on a sample of 222 articles published from 1996 to 2018 in international, peer-reviewed journals. The analysis of the sample involves two complementary approaches: the co-word technique to identify the thematic clusters as well as their relative standing and a critical reflection on the papers to explain the intellectual content of these thematic clusters. The results of the co-word analysis show that MSCF is a dynamic topic with a rich and complex structure that comprises five thematic clusters. The value chain, capability and volatility clusters showed research topics that were taking a central role in the discussion on MSCF but were not mature yet. The SC purchasing practices and SC planning clusters involved work that was more focused and could be considered more mature. These clusters were then integrated in a framework that built on the competence–capability perspective and identified the major structural and infrastructural elements of MSCF as well as its antecedents and consequences. This paper proposes an integrative framework helping managers keep track the various decisions they need to make to increase flexibility from the viewpoint of the entire value chain

Competing effects of pain and fear of pain on postural control in low back pain?

STUDY DESIGN. A cross-sectional, observational study. OBJECTIVE. To determine whether pain and fear of pain have competing effects on postural sway in patients with low back pain (LBP). SUMMARY OF BACKGROUND DATA. Competing effects of pain and pain-related fear on postural control can be proposed as the likely explanation for inconsistent results regarding postural sway in the LBP literature. We hypothesized that although pain might increase postural sway, fear of pain might reduce sway through an increased cognitive effort or increased cocontraction to restrict body movement. The cognitive strategy would be less effective under dual-task conditions and the cocontraction strategy was expected to be less effective when standing on a narrow base of support surface. METHODS. Postural sway was measured in combined conditions of base of support (full and narrow) and cognitive loading (single and dual tasks) in 3 experimental groups with current LBP, recent LBP, and no LBP. Sway amplitude, path length, mean power frequency, and sample entropy were extracted from center-of-pressure data. RESULTS. The current-LBP group and recent-LBP group reported significantly different levels of pain, but similar levels of pain catastrophizing and kinesiophobia. The current-LBP group tended to display larger sway amplitudes in the anteroposterior direction compared with the other 2 groups. Mean power frequency values in mediolateral direction were lower in patients with the current LBP compared with recent LBP. Smaller sample entropy was found in the current-LBP group than the other groups in most experimental conditions, particularly when standing on a narrow base of support. CONCLUSION. Alterations of postural sway are mostly mediated by pain but not pain-related fear. LBP tends to increase sway amplitude, which seems to be counteracted by increased effort invested in postural control leading to decreased frequency and increased regularity of sway particularly under increased task demands. Level of Evidence: Cross-sectional study